Brushcutters of the type described above have cutting tools in the form of a circular knife or a star-shaped knife. The cutting tool can also be a rotating plastic filament which is metered from a supply spool as required. The drive shaft which leads from the motor shaft to the cutting tool is relatively long and is loaded by the weight of the motor under operating conditions. This causes transverse forces to develop which lead to constraints in the connection between the motor shaft and the drive shaft. The vibrations occurring in this manner are troublesome for the operator of the portable tool and can not be adequately damped by means of a damping member because to motor shaft and the drive shaft do not maintain their predetermined aligned end position. The vibrations which occur for example in the frequency range of between 800 to over 1300 Hertz also load the supporting tube and the bearing means of the drive shaft. The vibrations lead to a premature tiring of the operator and cause an increased wear of the portable tool.